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# Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

## Abstract

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from −5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

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## Acknowledgements

The authors appreciate helpful discussions with C. Stampfer, H. Bluhm, R. Bindel, M. Liebmann and K. Flöhr as well assistance during the measurements by A. Georgi. N.M.F., P.N.-I. and M.M. acknowledge support from the European Union Seventh Framework Programme under Grant Agreement no. 696656 (Graphene Flagship) and the German Science foundation (Li 1050-2/2 through SPP-1459), L.A.C., J.B. and F.L. from the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF) through the SFB 041-ViCom and doctoral college Solids4Fun (W1243). TB calculations were performed on the Vienna Scientific Cluster. R.V.G., A.K.G. and K.S.N. also acknowledge support from the EPSRC (Towards Engineering Grand Challenges and Fellowship programs), the Royal Society, the US Army Research Office, the US Navy Research Office and the US Airforce Research Office. K.S.N. is also grateful to the ERC for support via Synergy grant Hetero2D. A.K.G. was supported by Lloyd's Register Foundation. P.N.-I. acknowledges support from the Hungarian Academy of Sciences Lendület under grant no. LP2017-9/2017.

## Author information

Authors

### Contributions

N.M.F. carried out the STM measurements with assistance of P.N.-I. and C.H. and evaluated the experimental data under supervision of P.N.-I. and M.M. P.N.-I. performed the strain calculations, while T.R., F.L., and L.A.C. contributed DFT and TB calculations. C.R.W., Y.C., R.V.G., A.K.G. and K.S.N. provided the sample. M.M. conceived and coordinated the project together with N.M.F., P.N.-I. and F.L. The comparison between theory and experiment was conducted by N.M.F., M.M., F.L. and P.N.-I. M.M., N.M.F., P.N.-I. and F.L. wrote the manuscript with contributions from all authors.

### Corresponding author

Correspondence to Markus Morgenstern.

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## Supplementary information

### Supplementary Information

Supplementary Figures 1–8, Supplementary Text, Supplementary References.

### Supplementary Video 1

Evolution of the wavefunctions of the valley states when moving the quantum dot through the graphene–boron-nitride structure

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Freitag, N.M., Reisch, T., Chizhova, L.A. et al. Large tunable valley splitting in edge-free graphene quantum dots on boron nitride. Nature Nanotech 13, 392–397 (2018). https://doi.org/10.1038/s41565-018-0080-8

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